I presume this connects SSH clients, and serves a fake web page to browsers?
Sounds pretty cool, but do SSH clients (e.g. PuTTY need special support for it)
Nope, no support needed. SSLH will proxy SSL traffic to whatever other SSL service you have running (nginx, openvpn, etc.), and send the SSH traffic to openssh. It look like it even supports recognizing plain HTTP traffic as well and proxying it accordingly.